Calculus Review for Flashcard 12. Chain Rule (Updated)

Front

Find the 2nd derivative of f(x) = 4cos(7x)

Back

-196cos(7x)

Front

Find the derivative: y=(5x^3 + 3)^8

Back

dy/dx= 120x^2 (5x^3 + 3)^7

Front

Differentiate y = (x^3 – 13)^5 with respect to x

Back

15x^2(x^3 – 13)^4

Front

Find the derivative of f(x) = 4sin(7x+1)

Back

28cos(7x+1)

Front

Find the derivative of f(x) = 4cos(7x)

Back

-28sin(7x)

Front

What is the Chain Rule in calculus?

Back

The Chain Rule is a formula for computing the derivative of the composition of two or more functions.

Front

State the formula for the Chain Rule.

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

Differentiate y = (3x^2 + 2)^4

Back

dy/dx = 24x(3x^2 + 2)^3

Front

What is the derivative of sin(kx)?

Back

The derivative is kcos(kx).

Front

What is the derivative of cos(kx)?

Back

The derivative is -ksin(kx).